How to find the common part with a Venn Diagram - ISEE Lower Level Quantitative Reasoning
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Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
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Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group 
represents the respondents that answered "yes" to the survey question. Group 
represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What percentage of the respondents answered "maybe" to Aracely's survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What percentage of the respondents answered "maybe" to Aracely's survey question?
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly 
percent of the respondents answered "yes" or "no" to the question
.
The solution is the total percent population take away the percent that answered "yes" or "no":
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly
The solution is the total percent population take away the percent that answered "yes" or "no":
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The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category 
represents the number of players on the team that are left-handed.
Category 
represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that 
and that there are 
players in the overlapping region of the diagram.
What fraction of the players are left-handed pitchers?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
What fraction of the players are left-handed pitchers?
Since there are 
left-handed pitchers and 
total players that are either left-handed, pitchers or both the solution is:
Since there are
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The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
Compare your answer with the correct one above
The Venn diagram above represents the results from a recent survey given to middle school students. Category represents the amount of students that only like pizza. Category represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
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If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
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Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
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Thirty people are surveyed concerning their color preference. Eighteen people like blue, twenty-one like pink, and six don't like either color. How many people like both colors?
Thirty people are surveyed concerning their color preference. Eighteen people like blue, twenty-one like pink, and six don't like either color. How many people like both colors?
Start by removing the number who don't like either from the total number of peole surveyed:
Using set notation we get:
, or the number of people who like both colors, 
, is equal to the number of people who like blue, 
, plus the number of people who like pink, 
, minus the number of people who like both blue and pink, 
.
Start by removing the number who don't like either from the total number of peole surveyed:
Using set notation we get:
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Twenty-five students were surveyed concerning a classroom pet. Thirteen students wanted a lizard, fifteen wanted a frog, and five didnt want a pet at all. How many students wanted both a lizard and a frog?
Twenty-five students were surveyed concerning a classroom pet. Thirteen students wanted a lizard, fifteen wanted a frog, and five didnt want a pet at all. How many students wanted both a lizard and a frog?
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we get:
, or the number of people who like both pets, 
, is equal to the number of people who like frogs, 
, plus the number of people who like lizards, 
, minus the number of people who like both frogs and lizards, 
.
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we get:
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Fifty people were surveyed. Twenty-three people liked the baseball team from Chicago, thirty-five like the baseball team from St. Louis, and ten don't like either team. How many people like both teams?
Fifty people were surveyed. Twenty-three people liked the baseball team from Chicago, thirty-five like the baseball team from St. Louis, and ten don't like either team. How many people like both teams?
Start by removing the number who don't like either team from the total number of people surveyed:
Using set notation we get:
, or the number of people who like both teams, 
, is equal to the number of people who like the Cubs, 
, plus the number of people who like the Cardinals, 
, minus the number of people who like both teams, 
.
Start by removing the number who don't like either team from the total number of people surveyed:
Using set notation we get:
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Twenty-five students are surveyed. Twelve students like math, fifteen like science, and six don't like either subject. How many students like both math and science?
Twenty-five students are surveyed. Twelve students like math, fifteen like science, and six don't like either subject. How many students like both math and science?
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we have:
, or the number of people who like both subjects, 
, is equal to the number of people who like math, 
, plus the number of people who like science, 
, minus the number of people who like both math and science 
.
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we have:
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Fifty people are surveyed at the zoo. Thirty-seven liked the Great Apes, twenty-two liked the Reptile House, and eleven didn't like either. How many people liked both the Great Apes and the Reptile House?
Fifty people are surveyed at the zoo. Thirty-seven liked the Great Apes, twenty-two liked the Reptile House, and eleven didn't like either. How many people liked both the Great Apes and the Reptile House?
Start by removing the number who don't like either from the total number of people surveyed:
Using set notation we have:
, or the number of people who like both animals, 
, is equal to the number of people who like apes, 
, plus the number of people who like reptiles, 
, minus the number of people who like both apes and lizards, 
.
Start by removing the number who don't like either from the total number of people surveyed:
Using set notation we have:
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Use the following Venn Diagram to answer the question.
What hobbies to both Andy and Mary enjoy?
Use the following Venn Diagram to answer the question.
What hobbies to both Andy and Mary enjoy?
A Venn Diagram is made up of two circles. Each circle represents something, and the section where they intersect shows what those two circles have in common. So, in the Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. The section in the middle shows the hobbies Andy and Mary have in common.
So, to answer the question, what hobbies do Andy and Mary have in common, we can see that they both enjoy eating and singing.
A Venn Diagram is made up of two circles. Each circle represents something, and the section where they intersect shows what those two circles have in common. So, in the Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. The section in the middle shows the hobbies Andy and Mary have in common.
So, to answer the question, what hobbies do Andy and Mary have in common, we can see that they both enjoy eating and singing.
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Use the following Venn Diagram to answer the question.
What hobbies do Andy and Mary have in common?
Use the following Venn Diagram to answer the question.
What hobbies do Andy and Mary have in common?
Let's look at the Venn Diagram.
We can see the first circle contains Andy's hobbies, and the second circle contains Mary's hobbies. The place in the middle, where the 2 circles intersect, shows the hobbies that both Andy and Mary enjoy. Or the hobbies they have in common. You can see they are a part of each person's circle.
So, the hobbies that are in the middle are eating and singing. Therefore, the hobbies that Andy and Mary have in common are eating and singing.
Let's look at the Venn Diagram.
We can see the first circle contains Andy's hobbies, and the second circle contains Mary's hobbies. The place in the middle, where the 2 circles intersect, shows the hobbies that both Andy and Mary enjoy. Or the hobbies they have in common. You can see they are a part of each person's circle.
So, the hobbies that are in the middle are eating and singing. Therefore, the hobbies that Andy and Mary have in common are eating and singing.
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Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
Compare your answer with the correct one above
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group represents the respondents that answered "yes" to the survey question. Group represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What percentage of the respondents answered "maybe" to Aracely's survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What percentage of the respondents answered "maybe" to Aracely's survey question?
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly percent of the respondents answered "yes" or "no" to the question
.
The solution is the total percent population take away the percent that answered "yes" or "no":
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly
The solution is the total percent population take away the percent that answered "yes" or "no":
Compare your answer with the correct one above
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category represents the number of players on the team that are left-handed.
Category represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that and that there are players in the overlapping region of the diagram.
What fraction of the players are left-handed pitchers?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
What fraction of the players are left-handed pitchers?
Since there are left-handed pitchers and total players that are either left-handed, pitchers or both the solution is:
Since there are
Compare your answer with the correct one above
The Venn diagram above represents the results from a recent survey given to middle school students. Category represents the amount of students that only like pizza. Category represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
Compare your answer with the correct one above
The Venn diagram above represents the results from a recent survey given to middle school students. Category represents the amount of students that only like pizza. Category represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
Compare your answer with the correct one above
If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
Compare your answer with the correct one above